Consider the following matrix A and its reduced row-echelon form: 5-6 103 2 12 -3-69 12-15 18 0 1 -3 -3 2-4 -1 0-3 -2 -1 -2 0 0 0 -6-9 9 15 -24 24 000 A= 1 2-3-4 Basis for row(A): Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 2 1 0 2 1 2 Basis for null(A): 0 1 -3 -3 Dimension of null(A): 1 0 {}} Basis for col(A): 2 Dimension of col(A): 1 {]} rref(A): 000 000
Consider the following matrix A and its reduced row-echelon form: 5-6 103 2 12 -3-69 12-15 18 0 1 -3 -3 2-4 -1 0-3 -2 -1 -2 0 0 0 -6-9 9 15 -24 24 000 A= 1 2-3-4 Basis for row(A): Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 2 1 0 2 1 2 Basis for null(A): 0 1 -3 -3 Dimension of null(A): 1 0 {}} Basis for col(A): 2 Dimension of col(A): 1 {]} rref(A): 000 000
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please find the following:
Dimension of null(A):
Basis for null(A):
Dimension of col(A):
Basis for col (A):
![Consider the following matrix A and its reduced row-echelon form:
1 2 -3 -4 5 -6
-3 -6 9 12 -15 18
-1 0-3 -2 -1 -2
-6-9 9 15 -24 24
Basis for row(A):
Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them.
Dimension of row(A): 2
1
032
1
2
Basis for null(A):
Official T
Dimension of null(A): 1
Basis for col(A):
0
1
-3
0
2
Dimension of col(A): 1
{]}
rref(A)
10 3 21 2
0 1-3-3 2-4
0 0 0 000
0 0 0
000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ae66eef-1409-41c4-be9d-744d399de224%2F4f5e5fa9-0e42-424d-a1cd-0bfefa2c29ff%2F4t3vgi3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following matrix A and its reduced row-echelon form:
1 2 -3 -4 5 -6
-3 -6 9 12 -15 18
-1 0-3 -2 -1 -2
-6-9 9 15 -24 24
Basis for row(A):
Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them.
Dimension of row(A): 2
1
032
1
2
Basis for null(A):
Official T
Dimension of null(A): 1
Basis for col(A):
0
1
-3
0
2
Dimension of col(A): 1
{]}
rref(A)
10 3 21 2
0 1-3-3 2-4
0 0 0 000
0 0 0
000
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